Components of a conventional projection lithographic system 80 are shown in FIG. 1. An illumination controller 20 drives an illumination source 30 to illuminate a mask 40 or reticle. The mask includes features that act to diffract the illuminating radiation through a pupil 50 which may control directional extent of the illumination, and through a lens 60 onto an image plane such as a semiconductor wafer 70. The wafer 70 typically includes a resist (photoactive material). When the resist is exposed to the projected image, the developed features in the resist closely conform to the desired patterns that form a target image, which is thus transferred to the wafer 70. The pattern of features on the mask 40 acts as a diffracting structure analogous to a diffraction grating. Increased precision in the formed circuitry depends on the intensities of the illumination that strikes different positions of the wafer 70.
There is increasing interest in methods to optimize the illumination distributions, or sources, used in photolithography to provide for small structures. Exemplary U.S. patents include U.S. Pat. No. 5,680,588, “Method and System for Optimizing Illumination in an Optical Photolithography Projection Imaging System,” issued to Gortych et al., Oct. 21, 1997; U.S. Pat. No. 6,563,566, “System and Method for Printing Semiconductor Patterns Using an Optimized Illumination and Reticle” issued to Rosenbluth et al., May 13, 2003; and U.S. Pat. No. 7,057,709, “Printing a mask with maximum possible process window through adjustment of the source distribution” issued to Rosenbluth, Jun. 6, 2006.
Other relevant publications include: “Illuminator design for the printing of regular contact patterns,” M. Burkhardt et al., Microelectronic Engineering, v. 41-42 (1998): p. 91.; “The Customized Illumination Aperture Filter for Low k1 Photolithography Process,” T.-S. Gau et al., SPIE v. 4000—Optical Microlithography XIII, ed. C. P. Progler (Santa Clara, Calif.: SPIE, 2000), p. 271.; “Optimum Mask and Source Patterns to Print a Given Shape,” A. E. Rosenbluth, et al., JM31, no. 1 (2002): p. 13; and “Global optimization of the illuminator distribution to maximize integrated process window”, A. E. Rosenbluth and N. Seong, SPIE v. 6154 (2006).
Future generations of projection lithography systems will rely heavily on intensively customized sources to increase the quality of the printing system. Intensively customized sources can be realized physically by using, for example, Diffractive Optical Elements (DOEs). Exploiting such sources by using methods for determining a source distribution provides specialized benefit to photolithographic applications. These methods are referred to as source optimization methods. The intensity distribution provided by a DOE can be optimized with many more degrees of freedom than conventional illumination patterns.
Complex sources involving multiple disconnected lobes are known to improve lithographic performance. Optimizing such shapes often involves making assumptions about the basic topology of the desired source pattern, e.g., the number of separate lobes. Indeed, any method based on local optimization involves refinement from an assumed initial starting design. The above-referenced publication entitled “Optimum Mask and Source Patterns to Print a Given Shape” introduced the idea of globally optimizing the source, i.e., finding the optimum shape without assuming a starting design, and doing so in a way that maximizes a bona fide lithographic metric, rather than by employing mere heuristic assessments. The objective function (merit function), considered in that publication, is directed to obtaining the largest possible exposure latitude in focus, e.g., attaining the sharpest possible focused image.
U.S. Pat. No. 7,057,709 and the publication entitled “Global optimization of the illuminator distribution to maximize integrated process window” describe methods for extending the approach in “Optimum Mask and Source Patterns to Print a Given Shape” to optimize for a maximum possible process window through focus. The so-called ED-window (exposure defocus) analysis is a convenient way to assess lithographic quality that takes both exposure latitude and Depth of Focus (DOF) into account. The integrated area of the ED-window is in turn a very useful single-parameter metric for assessing overall image quality (see “Level-specific lithography optimization for 1-Gb DRAM,” A. K. Wong et al., IEEE Transactions on Semiconductor Manufacturing 13, no. 1 (February 2000): p. 76.).
Optimization for providing a maximum process window has been achieved through transformation of percentage dose latitude to arrive at a reformulation as a near linear programming problem (see U.S. Pat. No. 7,057,709 and the publication entitled “Global optimization of the illuminator distribution to maximize integrated process window”). This reformulated problem uses variables representing a scaled version of the unknown source intensities together with additional auxiliary variables, which are defined to monitor the problem's process window. The objective function is then defined to maximize the process window (see “Global optimization of the illuminator distribution to maximize integrated process window”). However, the linear form of the transformed variables does not precisely represent these quantities except in the final optimized solution. Therefore, there is no straightforward application of this method to different lithographic problems.
The above-mentioned optimization is limited in that, as far as each individual mask pattern in the set being optimized is concerned, it is formulated only to maintain a single stabilized 2D image design through focus or through resist depth. This is a classic problem in lithographic image formation, in which the goal is to produce a certain image shape as sharply as possible and to maintain that shape through a large depth of focus. Standard photoresist layers are almost binary in their interaction with the image, which means that the attained image shape is converted to a set of near-vertical-sided openings in the resist film after the resist is developed. To a good approximation, cross sections of the post-develop resist thickness exhibit a binary or tophat character in the classical lithographic scenario, and, in many cases, a perfect tophat shape is acceptable.
However, when adopting a broader definition of lithographic processing, more complex situations occur in which it is advantageous to print openings in the film whose cross-sections through depth take on a prescribed non-binary character. An example of this is a dual damascene structure used commonly for metal interconnects in ultra-large scale integrated circuits. FIG. 2 shows the ‘T’-like structure 100 that is preferred. When printing such openings using a single exposure, it is preferred to use a controlled dose profile through the depth of the resist. More precisely, there needs to be a way to expose the resist with a three-dimensional dose profile that approaches a prescribed dose profile under as large a range of fluctuations in exposure time and lens focus as possible (e.g., maintain tolerance over as large a lithographic process window as possible).
One problem is that under non-tophat applications the state-of-the-art source optimization approach, such as shown in U.S. Pat. No. 7,057,709 and the publication entitled “Global optimization of the illuminator distribution to maximize integrated process window”, no longer applies. Using such a method for a pure tophat target profile one could define auxiliary variables using constraints that involved only the intensity, e.g., constraints that are independent of the resist sensitivity. Moreover, the constraints on the image itself only refer to intensities normalized to an anchor dose. It is only under these conditions that a near linear-programming problem may be shown to be sufficient for calculating the globally optimum source. With the previously considered tophat target profiles, this source optimization approach was constructed such that the act of optimizing an objective function which involved the auxiliary variables would inherently push these variables to values that defined a process window. Moreover, as a consequence of being optimized, the function would converge to the optimized process window. However, lithographic processes like those described in “Method for fabricating dual damascene structures”, M. E. Colburn et al., US Pat. Publ. No. 2005/0202350, require target profiles that are not tophat.
The core notion of a lithographic process window, whose optimization is desired, was developed in the context of a low-NA (numerical aperture) procedure, where the resist image could be imagined to propagate in air. Under such circumstances there is no distinction between a change in lens focus (which may equivalently be caused by a fluctuation in wafer height) and a change in z-location within the “resist layer”, which is simply the focal region of the aerial image in this elementary case, at which printing is evaluated. However, in current lithographic simulations it is often necessary to take into account the detailed optical properties of the resist film stack, which in effect introduces severe aberrations. Under such conditions, a change in depth within the resist layer is no longer equivalent to a change in focus. Moreover, when the wafer is at nominal focus, the character of the image above the resist stack and the character of the image below the stack can both affect the quality of the exposing image when focus fluctuations shift the wafer stack away from nominal, particularly if quality is assessed by averaging across the layer thickness.
One way to achieve a desired three-dimensional topology is to use multiple layers with varying sensitivity and to expose them using multiple exposures. In many cases the desired profile is stepped in depth; otherwise a large number of layers (physically, or in simulation) can produce a stepped approximation to the desired profile.
Such a process is the subject of U.S. Pat. Publ. No. 2005/0202350 and is illustrated in FIG. 2. In that embodiment two resist layers 110 and 120 are placed on top of the non-photosensitive process film to be patterned 130. The two resist layers 110 and 120 are given different sensitivities; the top layer 110 would typically be given a higher sensitivity than the bottom layer 120, which means that its dose-to-clear value would be lower. The resist stack is then exposed with a mask 40 that will print the features desired in the top layer 110, but with only as much dose as is needed to develop the feature profile shown in the top layer 110. This first exposing dose is not sufficient to produce an above-threshold exposure in the bottom layer 120. A second exposure is then done with a mask 40 which prints the features desired in the second layer 120 of resist, but this time with a higher dose, i.e., high enough to have the bottom layer 120 develop though. When the structure is then developed the result is the ‘T’ dual damascene profile 100.
Producing an aerial image that would give the correct profile after a single exposure and development of a single layer of resist is very difficult. To print the structure in one exposure, a mask 40 must be made that will produce lower dose factors in the areas where only the top layer 110 is intended to develop. One possible technique to accomplish this may be to use mask optimizations, such as a grey level mask, to reduce the intensity transmission in those areas. However, there remains a need for finding the best source for printing such a 3D structure, while taking into account the different resist sensitivity levels through depth. In analyzing such a process one would have to consider that the developed contour will not purely follow the sensitivity profile, since the optical image changes structure as it propagates through the resist stack.
As should be apparent, there is a need for new near linear programming methods for determining source optimization for three-dimensional designs.